Uniform Cluster Traffic Model on Closed Two-Contours System with Two Non-symmetrical Common Nodes

摘要

Spontaneous transitions of traffic flows, from the laminar state to the turbulent state, may occur. In 2008, the experimental results of traffic jam formation on a ring was published by Y. Sugiyama et al. Our paper studies a dynamical system which contains two closed contours with two common points (nodes). The nodes divide each contour into two parts with lengths d and 1 - d. In each contour, there is a moving segment called a cluster. The clusters move in accordance with given rules. The system can be intepreted as a traffic model and belongs to the class of dynamical systems introduced by A.P. Buslaev. We study the system spectrum connected with the set of cyclic trajectories in the system state space. Some theorems regarding the spectrum have been proved.